No, you can't delete the "liked that you viewed their profile" and "liked that you viewed their photo" notices. Or at least, I can't. Maybe that is an Extras option? What I can do is hide all their activity. But then if they actually do like or comment on something, it won't show in my feed.
No, you can't hide your activities from others. I've looked and could not find a setting for that. Since you mentioned it, I thought that it could be an Extras setting, but support says there is no such setting.
I've done some testing and I think I see now why these notices might not be so annoying to others. For most, they are probably just mixed in with a sea of notices. For me, they are the only thing I see. I have set it so that we have 0 matches. I use our feed to read comments and preview messages. When I clear our notifications for messages, comments, and likes, our feed is empty. Or it used to be until these "liked that you viewed" notices started showing up.
Aside from disliking the clutter, I still think it's a bit creepy to "like" that someone glanced in your general direction. If I was interested, I would have liked something or commented on something or sent them a message. All I did was view the mini popup profile.
In any case, it's not the end of the world, but I am curious to know if anyone likes to have this info? If so, do you see it as flirting? Or what?